Am I right to be a bit miffed by this kind of thing that she does?

She probably has low self esteem and low confidence, so when you do go out and you don't pay she might not feel like she's been treated by you. however, after a while of been together it should be shared when it comes to paying for things. If you really want to be with this woman I would make her a meal, that way neither of you have to pay to go out but you're still treating her and making her feel special (which every girl wants to feel). If she carries on behaving the way she is then she's not worth your time or effort. Good luck